Probability, Confidence Interval & Hypothesis Testing

See attached file for 3 problems: Tesla Motors, PC manufacturer and large insurance company claims

4. Tesla Motors needs to buy axles for their new car. They are considering using Chris Cross Manufacturing as a vendor. Tesla's requirement is that 95% of the axles are 100 cm ± 2 cm. The following data is MegaStat output from a test run from Chris Cross Manufacturing. Should Tesla select them as a vendor? Explain your answer.

Descriptive statistics

count 16
mean 99.938
sample variance 2.313
sample standard deviation 1.521
minimum 97
maximum 102.9
range 5.9

population variance 2.169
population standard deviation 1.473

standard error of the mean 0.380

tolerance interval 95.45% lower 96.896
tolerance interval 95.45% upper 102.979
half-width 3.042

1st quartile 98.900
median 99.850
3rd quartile 100.475
interquartile range 1.575
mode 98.900

5. A PC manufacturer claims that no more than 5% of their machines are defective. In a random sample of 100 machines, it is found that 8.5% are defective. The manufacturer claims this is a fluke of the sample. At a .02 level of significance, test the manufacture's claim, and explain your answer..

MegaStat Output
Hypothesis test for proportion vs. hypothesized value

Observed Hypothesized
0.085 0.05 p (as decimal)
9/100 5/100 p (as fraction)
8.5 5.0 X
100 100 n

0.0218 std. error
1.61 Z
.0541 p-value (one-tailed, upper)

6. The following table gives the number of claims at a large insurance company by kind and geographical region.
East South
Midwest
West
Totals

Hospitalization
102
98
39
62
301

Physician's Visit
263
514
120
351
1248

Outpatient Treatment
100
226
65
99
490

Totals
465
838
224
512
2039

(A) Referring to the above table, if a bill is chosen at random, what is the probability that it is either from the East or from the West?
(B) Referring to the above table, given that the bill is from the Midwest, what is the probability that it is for a Physician's Visit?